To solve the equation cos(x) = cos(5x), we can use the identity cos(a) = cos(b) if and only if a = b + 2πn or a = -b + 2πn, where n is an integer.

In this case, we have cos(x) = cos(5x), so we can set x = 5x + 2πn or x = -5x + 2πn.

Simplifying the first equation, we get 4x = 2πn, which gives x = πn/2.

Simplifying the second equation, we get 6x = 2πn, which gives x = πn/3.

Therefore, the solutions to the equation cos(x) = cos(5x) are x = πn/2 and x = πn/3, where n is an integer.